Give Me But A Firm Spot On

It Follows At Once From The Last Proposition That The Centre Of Gravity Of Any Triangle Is At The Intersection Of The Lines Drawn From Any Two Angles To The Middle Points Of The Opposite Sides Respectively.

Archimedes To Eratosthenes Greeting. ... Certain Things First Became Clear To Me By A Mechanical Method, Although They Had To Be Demonstrated By Geometry Afterwards Because Their Investigation By The Said Method Did Not Furnish An Actual Demonstration. But It Is Of Course Easier, When We Have Previously Acquired By The Method, Some Knowledge Of The Questions, To Supply The Proof Than It Is To Find It Without Any Previous Knowledge.

There Are Things Which Seem Incredible To Most Men Who Have Not Studied Mathematics.

Those Who Claim To Discover Everything But Produce No Proofs Of The Same May Be Confuted As Having Actually Pretended To Discover The Impossible.

How Many Theorems In Geometry Which Have Seemed At First Impracticable Are In Time Successfully Worked Out!